W07D1
Magnetic Dipoles, Force and
Torque on a Dipole, Experiment 2
W07D1 Magnetic Dipoles, Torque and Force on a Dipole,
Experiment 2: Magnetic Dipole in a Helmholtz Coil
http://web.mit.edu/8.02t/www/materials/Experiments/expMagForcesDipoleHelmholtz.pdf
Reading Course Notes: Sections 8.4, 8.6.4, 8.10.4, 8.13, 9.5, 9.9
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Announcements
Exam Two Reviews:
Monday from 7-9 pm in 26-152
Tuesday from 9-11 pm in 26-152
Wednesday from 9-11 pm in 26-152
PS 6 due W07 Tuesday at 9 pm in boxes outside 32-082 or 26152
Exam 2 Thursday March 21 7:30 - 9:30 pm: See announcement
pages for section room assignments
Conflict Friday March 22 9-11 am in 32-082; 10-12 noon in 6-120
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Magnetic Field of Bar Magnet
(1) A magnet has two poles, North (N) and South (S)
(2) Magnetic field lines leave from N, end at S
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Magnetism – Bar Magnet
Like poles repel, opposite poles attract
4
Bar Magnets Are Dipoles!
• Create Dipole Field
• Rotate to orient with Field
Is there magnetic “mass”
or magnetic “charge?”
NO! Magnetic monopoles do not exist in isolation
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Magnetic Monopoles?
Magnetic Dipole
Electric Dipole
p
-q
m
q
When cut:
2 monopoles (charges)
When cut: 2 dipoles
Magnetic monopoles do not exist in isolation
Another Maxwell’s Equation! (2 of 4)
E

d
A


S
qin
0
Gauss’s Law
 B  dA  0
S
Magnetic Gauss’s Law
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Conservation of Magnetic Flux:
qin
 E  dA  
S
0
 B  dA  0
S
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Torque on a Current Loop in a
Uniform Magnetic Field
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Review: Magnetic Force on CurrentCarrying Wire
If the wire is a uniform magnetic field then
Fmag


   Id s   B
 wire

If the wire is also straight then
Fmag  I (L  B)
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Group Problem: Current Loop
Place rectangular current loop in uniform B field
1) What is the net force on
this loop?
2) What is the net torque
on this loop?
3) Describe the motion the
loop makes
ĵ
k̂
î
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Torque on Rectangular Loop
  IABjˆ
Area vector
A  Anˆ  abnˆ
k̂
ĵ x
î
nˆ  kˆ , B =B ˆi
  IA  B
No net force but there is a torque
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Magnetic Dipole Moment
r
  IA n̂  IA
http://web.mit.edu/viz/EM/visualizations/magnetostatics/calculatingMagneticFields/RingMagField/RingMagField.htm
Torque on Current Loop
Place rectangular current loop in uniform B field
Magnetic moment points
out of the page
  B
    B =  Bˆj  IABˆj
ĵ
k̂
î
torque tries to align the
magnetic moment vector
in the direction of the
magnetic field
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Concept Question: Magnetic Field
Lines
The picture shows the field lines outside a
permanent magnet The field lines inside the
magnet point:
1.
2.
3.
4.
5.
6.
Up
Down
Left to right
Right to left
The field inside is zero
I don’t know
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Concept Q. Answer: Magnetic Field Lines
Answer: 1. They point up inside the magnet
Magnetic field lines are continuous.
E field lines begin and end on charges.
There are no magnetic charges (monopoles)
so B field lines never begin or end
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Demonstration:
Deflection of a Compass Needle by a
Magnet G1
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%201&show=0
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Demonstration:
Galvanometer principle G10
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%2010&show=0
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Concept Question: Dipole in Field

From rest, the coil above will:
1.
2.
3.
4.
5.
6.
7.
8.
rotate clockwise, not move
rotate counterclockwise, not move
move to the right, not rotate
move to the left, not rotate
move in another direction, without rotating
both move and rotate
neither rotate nor move
I don’t know
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Concept Q. Answer: Dipole in Field
Answer: 1. Coil will rotate clockwise (not move)
No net force so no center of mass motion. BUT
Magnetic dipoles rotate to align with external
field (think compass)
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Force on a Dipole in a NonUniform Field
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Dipoles don’t move???
This dipole rotates but
doesn’t feel a net force
in a uniform magnetic
field
But dipoles can
feel magnetic
force.
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Dipoles in Non-Uniform Fields:
Magnetic Force
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Concept Question: Dipole in Field
The current carrying coil above will feel a net force
1.
2.
3.
4.
upwards
downwards
of zero
I don’t know
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Concept Q. Answer: Dipole in Field
Answer: 2. Feels downward force. The forces shown
dFmag  I (d s  B) produce a net downward force
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Force on Magnetic Dipole
N

S
N
S
What makes the field pictured? Bar magnet
below dipole, with N pole on top. It is aligned with
the dipole pictured, they attract!
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Work Done by Interaction to Anti-align
Magnetic Dipole
    B = - B sin  kˆ   zkˆ


W    z d     B sin  d   B cos 
0

0
 2 B
0
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Potential Energy: Dipole in Magnetic Field
 U  U (   )  U (  0)  W  2 B       B
Set zero reference point
U (   / 2)  0
U ( )     B
Lowest energy state (aligned) :
U (  0)    B
Highest energy state (anti-aligned): U (   )   B
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Force on Magnetic Dipole
N

S
N
S
Bz ˆ
F  (   B)   z
k
z
along z-axis
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Magnetic Field Profiles Experiment 2
Concept Question: Dipole in Helmholtz
A dipole pointing along
the positive x-direction
and located at the center
of a Helmholtz coil will
feel:
1.
2.
3.
4.
a force but not a torque.
a torque but not a force.
both a torque and a force.
neither force nor torque.
Concept Q. Answer: Dipole in Helmholtz
Answer: 2. a torque but not
a force. The Helmholtz coil
makes a UNIFORM FIELD.
Dipole feels only torque
(need gradient for force).
Concept Question: Dipole in AntiHelmholtz Coil
A dipole pointing along
the positive z-direction
and located at the center
of an anti- Helmholtz coil
will feel:
1.
2.
3.
4.
a force but not a torque.
a torque but not a force.
both a torque and a force.
neither force nor torque.
Concept Q. Answer: Dipole in AntiHelmholtz Coil
Answer: 1. A force
because there is a gradient
in the magnetic field but no
torque because the
magnetic field at the center
is zero.
Experiment 2:
Magnetic Forces on Dipole
in Fields of Helmholtz Coil
Getting Started: Set up current supply
• Open circuit (disconnect a lead)
• Turn current knob full CCW (off)
• Increase voltage to ~12 V
– This will act as a protection: V<12 V
• Reconnect leads in Helmholtz mode
• Increase current to ~1 A
Appendix Experiment 2:
Magnetic Forces on Dipole
in Fields of Helmholtz Coil
Field Configurations and Concept
Questions
Appendix 2:
Gauss’s Law for Magnetism
Animation: Magnetic Field Generated by
a Current Loop
http://web.mit.edu/viz/EM/visualizations/magnetostatics/calculatingMagneticFields/RingMagInt/RingMagIntegration.htm
38
Demonstration:
Magnetic Field Lines
from Bar Magnet G2
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%202&show=0
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